9000 (number) explained

Number:	9000
Roman:	M, or
Unicode:	M, m,,
Lang1:	Armenian
Lang1 Symbol:	Ք

9000 (nine thousand) is the natural number following 8999 and preceding 9001.

Selected numbers in the range 9001–9999

9001 to 9099

• 9001 – sexy prime with 9007
• 9007 – sexy prime with 9001
• 9009 – centered cube number
• 9025 = 95², centered octagonal number
• 9029 – Sophie Germain prime
• 9041 – super-prime
• 9045 – triangular number
• 9059 – Sophie Germain prime
• 9072 – decagonal number
• 9077 – Markov number^[1]
• 9091 – unique prime

9100 to 9199

• 9103 – super-prime
• 9126 – pentagonal pyramidal number^[2]
• 9139 – tetrahedral number^[3]
• 9175 – smallest (provable) generalized Sierpiński number in base 10: is always divisible by one of the prime numbers .^[4]
• 9180 – triangular number

9200 to 9299

• 9216 = 96²
• 9221 – Sophie Germain prime
• 9224 – octahedral number^[5]
• 9241 – cuban prime of the form x = y + 1
• 9261 = 21³, largest 4 digit perfect cube
• 9272 – weird number
• 9283 – centered heptagonal number
• 9293 – Sophie Germain prime, super-prime

9300 to 9399

• 9316 – triangular number
• 9319 – super-prime
• 9334 – nonagonal number
• 9349 – Lucas prime, Fibonacci number
• 9371 – Sophie Germain prime
• 9376 – 1-automorphic number
• 9397 – balanced prime

9400 to 9499

• 9403 – super-prime
• 9409 = 97², centered octagonal number
• 9419 – Sophie Germain prime
• 9439 – completes the twelfth prime quadruplet set
• 9453 – triangular number
• 9455 – square pyramidal number^[6]
• 9457 – decagonal number
• 9461 – super-prime, twin prime
• 9467 – safe prime
• 9473 – Sophie Germain prime, balanced prime, Proth prime
• 9474 – Narcissistic number in base 10
• 9479 – Sophie Germain prime
• 9496 – Telephone/involution number

9500 to 9599

• 9511 - prime number
• 9521 - prime number
• 9533 - prime number
• 9539 – Sophie Germain prime, super-prime
• 9551 – first prime followed by as many as 35 consecutive composite numbers
• 9587 – safe prime, follows 35 consecutive composite numbers
• 9591 – triangular number
• 9592 - amount of prime numbers under 100,000

9600 to 9699

• 9601 – Proth prime
• 9604 = 98²
• 9619 – super-prime
• 9629 – Sophie Germain prime
• 9647 – centered heptagonal number
• 9661 – super-prime, sum of nine consecutive primes (1049 + 1051 + 1061 + 1063 + 1069 + 1087 + 1091 + 1093 + 1097)
• 9689 – Sophie Germain prime
• 9699 – nonagonal number

9700 to 9799

• 9721 – prime of the form 2p-1
• 9730 – triangular number
• 9739 – super-prime
• 9743 – safe prime
• 9791 – Sophie Germain prime

9800 to 9899

• 9800 – member of a Ruth-Aaron pair (first definition) with 9801
• 9801 = 99², the largest 4 digit perfect square, centered octagonal number, square pentagonal number, member of a Ruth-Aaron pair (first definition) with 9800
• 9833 – super-prime
• 9839 – safe prime
• 9850 – decagonal number
• 9855 – magic constant of n × n normal magic square and n-Queens Problem for n = 27.
• 9857 – Proth prime
• 9859 – super-prime
• 9870 – triangular number
• 9871 – balanced prime
• 9880 – tetrahedral number^[7]
• 9887 – safe prime

9900 to 9999

• 9901 – unique prime, sum of seven consecutive primes (1381 + 1399 + 1409 + 1423 + 1427 + 1429 + 1433)^[8]
• 9905 – number of compositions of 16 whose run-lengths are either weakly increasing or weakly decreasing^[9]
• 9923 – super-prime, probably smallest certainly executable prime number on x86 MS-DOS
• 9949 – sum of nine consecutive primes (1087 + 1091 + 1093 + 1097 + 1103 + 1109 + 1117 + 1123 + 1129)
• 9973 – super-prime
• 9988 – number of prime knots with 13 crossings
• 9999 – Kaprekar number, repdigit

Prime numbers

There are 112 prime numbers between 9000 and 10000:^[10]

9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973

Notes and References

1. 3*x*y*z..
2. n^2*(n+1)/2..
3. C(n+2,3) = n*(n+1)*(n+2)/6..
4. GENERALIZED SIERPIŃSKI NUMBERS TO BASE b . Brunner, Amy . Caldwell, Chris K. . Krywaruczenko, Daniel . Lownsdale, Chris . 数理解析研究所講究録 [Notes from the Institute of Mathematical Analysis (in, New Aspects of Analytic Number Theory)] . . Kyoto . 1639 . 2009 . 69–79 . 2433/140555 . 38654417 .
5. n*(2*n^2 + 1)/3..
6. 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6..
7. Web site: Sloane's A000292 : Tetrahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
8. Web site: Sloane's A040017 : Unique period primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-14.
9. 2022-06-02.
10. Web site: Stein . William A. . William A. Stein . The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture . wstein.org . 10 February 2017 . 6 February 2021.